I want to make a sytem of equations has the form
$$\begin{cases}
a_1x^2+b_1y^2 + c_1xy+d_1x + e_1y+3=0,\\
a_2x^2+b_2y^2 + c_2xy+d_2x + e_2y+3=0.
\end{cases}$$
so that the given system of equations has always two solutions $(1,2)$ and $(3,4)$. I tried

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